1. Field of the Invention
The invention relates to the field of wireless Multiple-Input Multiple-Output (MIMO) communication systems. More particularly, the present invention relates to a method and apparatus for MIMO decoding with outputting soft decisions using the complex-valued integer lattices, specifically in the case of two transmitting and two receiving antennas.
2. Description of the Related Art
Multiple-Input Multiple-Output (MIMO) systems represent multiple-antenna receiving/transmitting systems that possess a series of advantages over conventional single-antenna systems. More particularly, the use of multiple-antenna systems allows increasing a communication channel capacity. Since each receiving antenna at a receiving side receives a signal being a superposition of signals transmitted by all transmitting antennas, in decoding the received signal it is necessary to take into account all elements of a channel matrix characterizing a signal propagation channel from a transmitter to a receiver.
There are many methods for signal decoding in a conventional MIMO system, such as a Zero Forcing (ZF), a Minimum Mean Square Error (MMSE), an Ordered Serial Interference Cancellation (OSIC) etc, most of which are lower in accuracy than the most optimal Maximum-Likelihood (ML) technique. Moreover, many methods require significant computational cost. The latter note is especially topical for the maximum-likelihood technique.
The use of techniques of Lattice Reduction (LR) is disclosed in decoding algorithms for MIMO systems. The same work notes that decisions obtained using the LR techniques are close to the ML decisions, and the computational complexity in this case is comparable with the complexity of the ZF and MMSE OSIC techniques.
A conventional method disclosed in U.S. Pat. No. 6,724,843. This method comprises estimating a communication channel, obtaining a channel matrix H, and decoding the received signal using the LR technique. Here, since the above LR technique was initially intended for real matrices and vectors, and the channel matrix of the communication system includes complex vectors, in order to transition from complex values to real ones, the “unfolding” transform has been proposed as in Equation 1 below:
                              H          →                      [                                                                                                    ⁢                                                                                  ⁢                    H                                                                                                              -                                                              ⁢                                                                                  ⁢                    H                                                                                                                                        ⁢                                                                                  ⁢                    H                                                                                                            ⁢                    H                                                                        ]                          ,                  x          →                      [                                                                                                    ⁢                    x                                                                                                                                        ⁢                    x                                                                        ]                          ,                            [                  Equation          ⁢                                          ⁢          1                ]            which maintains a result of the matrix-vector multiplication Hx. H refers to a channel matrix, x refers to a transmitted vector,  refers to a real part, and  refers to an imaginary part.
The method proposed in U.S. Pat. No. 6,724,843 utilizes an LLL transform for the basis reduction of the vector space of columns of the channel matrix H. The original basis is formed by columns of the matrix Q from the QR-decomposition of the channel matrix H. The LLL transform consists of two main procedures:
decreasing sequentially the off-diagonal elements of the matrix R, meanwhile performing elementary transformations of columns [3, 5], carrying out the check of the so called reducedness ratio
            r      kk      2        +          r                        k          -          1                ,        k            2        ≥            3      4        ⁢          r                        k          -          1                ,                  k          -          1                    2      which could be interpreted as a relative growth of diagonal and neighbor to diagonal elements of the matrix R depending on their column indices, where ri,j refers to an element of the matrix R in the QR-decomposition. If the reducedness ratio is not accomplished, a second procedure is carried out, otherwise the process proceeds to the next column;
carrying out a transposition of two adjacent columns k−1, k of the matrix R (herewith, the triangularity of the R is deteriorated) and optional transformation that recovers the triangle form of the R. In so doing, it is possible that the reducedness ratio for the columns k−2, k−1 is deteriorated. In this case, the second procedure is carried out for them, too. Thus, the second procedure can be spread onto any of columns already processed at the step 1. As a result, diagonal elements of the columns 1, . . . , k of the R are obtained in ascending order in the sense of the reducedness ratio.
The disadvantage of the method described in U.S. Pat. No. 6,724,843 is in its great computational complexity due to several facts. First, the real channel matrix that is formed as a result of the “unfolding” has a great size, and the QR-decomposition requires computations proportional to the third power of this size. Second, the procedure of the column transposition with the subsequent recovering of the R triangularity associated with the reduction procedure is carried out multiple times and is also therefore costly from the computational viewpoint.
Another disadvantage relates to the type of the obtained decision. The method of U.S. Pat. No. 6,724,843 is a method of the V-BLAST type, i.e., the symbol decoding happens sequentially, layer by layer, by rounding to the nearest element of the modulation map. Symbols thus obtained are commonly referred to as hard decisions. The disadvantage of the V-BLAST is in propagating an error that appears due to a wrong symbol decoding in one of the layers to all subsequent layers. The wrong decoding occurs when the element of the modulation map nearest to the calculated symbol value does not coincide with the actually transmitted symbol. Since the rounding process affects nontrivially onto decoding in the subsequent layers, it is very difficult to build a correct estimation of the probability of the bit output decision (which estimation is also referred to as a soft decision). Thus, in many realizations, V-BLAST yields only hard decisions when the bit probability is not taken into account at all. Other methods, for example ML and modifications thereof, comprise the probabilistic error estimation and yield soft decisions, but the complexity of these techniques in comparison with the conventional MMSE detector is extremely high.
Many methods for correcting errors, such as convolution codes, turbo codes, low-density parity check codes, exist which are used in modern communication systems and which allow correcting errors effectively at the output of MIMO decoders. All of them work much more effectively when soft bit decisions having correctly calculated probability of the output bits are entered as the input data. Thus, the problem of obtaining correct soft decisions at the output of the MIMO decoder becomes very important. Not less important is to keep the computational complexity of the MIMO decoder at the level of ZF OSIC or MMSE OSIC filters.
Accordingly, there exists a need for a decoding apparatus and method for reducing the computational complexity while obtaining sufficient performance in a LR wireless communication system.